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%I #5 Sep 12 2013 15:52:23
%S 2,0,6,-2,2,16,0,-10,10,40,2,-2,-36,36,96,0,14,-14,-112,112,224,-2,2,
%T 64,-64,-320,320,512,0,-18,18,240,-240,-864,864,1152,2,-2,-100,100,
%U 800,-800,-2240,2240,2560,0,22,-22,-440,440,2464,-2464,-5632,5632,5632,-2,2,144,-144,-1680,1680,7168,-7168,-13824,13824
%N Triangle T(n,k) = A053120(n+2,k)-2*A053120(n+1,k)+A053120(n,k) read by rows, 0<=k<n.
%C Second differences downwards columns of the Chebyshev triangle A053120.
%C Row sums are 2, 6, 16, 40, 96, 224, 512, 1152, 2560, 5632, 12288,..., A057711.
%e 2;
%e 0, 6;
%e -2, 2, 16;
%e 0, -10, 10, 40;
%e 2, -2, -36, 36, 96;
%e 0, 14, -14, -112, 112, 224;
%e -2, 2, 64, -64, -320, 320, 512;
%e 0, -18, 18, 240, -240, -864, 864, 1152;
%e 2, -2, -100, 100, 800, -800, -2240, 2240, 2560;
%e 0, 22, -22, -440, 440, 2464, -2464, -5632, 5632, 5632;
%e -2, 2, 144, -144, -1680, 1680, 7168, -7168, -13824, 13824, 12288;
%t Clear[T, D2, x, n, m] T[n_, m_] := CoefficientList[ChebyshevT[n + 1, x], x][[m + 1]]; D2[n_, m_] := T[n + 2, m] - 2*T[n + 1, m] + T[n, m]; a = Table[Flatten[Table[D2[n, m], {m, 0, n}]], {n, 0, 10}]; Flatten[a]
%K tabl,sign
%O 1,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Jul 21 2008